Solve for x. (x-3)/(4)+(1)/(10)=(x+7)/(20) Answer:

Find Common Denominator: Find a common denominator for the fractions to combine them. The common denominator for 4, 10, and 20 is 20. Multiply each term by 20 to eliminate the denominators. 20 * ((x-3)/4) + 20 * (1/10) = 20 * ((x+7)/20)Simplify Terms: Simplify each term. (20/4) * (x-3) + (20/10) * 1 = (20/20) * (x+7) 5(x-3) + 2 = x+7Distribute and Combine: Distribute the 5 into the parentheses. 5x - 15 + 2 = x + 7Combine Like Terms: Combine like terms on the left side. 5x - 13 = x + 7Isolate x Term: Subtract x from both sides to get all x terms on one side. 5x - x - 13 = x - x + 7 4x - 13 = 7Solve for x: Add 13 to both sides to isolate the x term. 4x - 13 + 13 = 7 + 13 4x = 20Divide both sides by 4 to solve for x. 4x/4 = 20/4 x = 5

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(x-3)/(4)+(1)/(10)=(x+7)/(20)
Answer:

Solve for $\mathrm{x}$ . $\newline$ $\frac{x-3}{4}+\frac{1}{10}=\frac{x+7}{20}$ $\newline$ Answer:

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Math Problems

Grade 8

Solve equations with the distributive property

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Q. Solve for

\mathrm{x}

\newline

\frac{x-3}{4}+\frac{1}{10}=\frac{x+7}{20}

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions to combine them. $\newline$ The common denominator for $4$ , $10$ , and $20$ is $20$ . Multiply each term by $20$ to eliminate the denominators. $\newline$ $20 \times \left(\frac{x-3}{4}\right) + 20 \times \left(\frac{1}{10}\right) = 20 \times \left(\frac{x+7}{20}\right)$
Simplify Terms: Simplify each term. $\newline$ $(\frac{20}{4}) \cdot (x-3) + (\frac{20}{10}) \cdot 1 = (\frac{20}{20}) \cdot (x+7)$ $\newline$ $5(x-3) + 2 = x+7$
Distribute and Combine: Distribute the $5$ into the parentheses. $5x - 15 + 2 = x + 7$
Combine Like Terms: Combine like terms on the left side. $5x - 13 = x + 7$
Isolate x Term: Subtract $x$ from both sides to get all $x$ terms on one side. $\newline$ $5x - x - 13 = x - x + 7$ $\newline$ $4x - 13 = 7$
Solve for x: Add $13$ to both sides to isolate the $x$ term. $\newline$ $4x - 13 + 13 = 7 + 13$ $\newline$ $4x = 20$
Solve for x: Add $13$ to both sides to isolate the $x$ term. $\newline$ $4x - 13 + 13 = 7 + 13$ $\newline$ $4x = 20$ Divide both sides by $4$ to solve for $x$ . $\newline$ $\frac{4x}{4} = \frac{20}{4}$ $\newline$ $x = 5$